[vox-tech] OT math question

[Jeff Newmiller]

On Wed, 10 Nov 2004, Dylan Beaudette wrote:

> I know this is quite off topic... however it deals with numbers generated by a 
> computer, so....

*snicker*

Well, given that part of my job is analyzing insolation data, I might
as well weigh in on this, and it isn't any more off topic than many
other threads we've tackled here.

> So I have some solar insolation values- 1 value per day for an entire year. 

1) Insolation is often (almost always?) presented in units of kWh/m2/day
... since the standard "one sun" irradiance value is 1000 W/m2, these
preferred units can be reinterpreted as sun-hours/day (hours per day that
the sun could have shined at full power and obtained the same total
insolation).

> the graph of solar insolation (y-axis) vs. day of year (x-axis) vary in shape 
> - sometime looking very similar to a Gaussian distribution. I would like to 
> characterize the relative fatness of these "Gaussian-like" graphs with 
> something like a coefficient of variation... however, to the best of my 
> knowledge things like the CV operate on frequency distributions, which in 
> this case would only be characterizing the variation within the insolation 
> values with respect to eachother.

2) Gaussians are just mathematical curves that happen to fit frequency
data.  However, I think the interesting information in these plots would
be lost by imagining these curves to be comparable to nice, ideal
Gaussian distributions... for example, one characteristic of Gaussians is
that they apply over an infinite input range... your input range repeats
(every year), so in reality these humps are part of a repeating pattern.

> just for reference a sample image can be found here:
> http://169.237.35.250/~dylan/solar/index.html#more

3) I would guess that the green and orange curves [1] represent locations
in valleys. Noting how many days the insolation is less than some value
could be useful. The threshold value would depend on the purpose to which
the data are being applied... I would guess that less than half an hour
per day of full sunlight would be pretty useless for most energy analysis
purposes (such as building heating load or photovoltaic energy
conversion).  For curves that don't reach the threshold, noting the
minimum value could be useful.

4) The flatness at the top of some of the curves [2] is puzzling... almost
like there is an overhang that creates more shadow in the summer, though I
am having a hard time guessing how you would see that from an aerial view
(tall trees with a significant height to their lowest branches, casting
shadows nearby in the summer but further away in winter?).  A simple
characterization of this feature would be what the maximum value is, but
identifying the duration of flatness at the peak might be accomplished by
determining how long the curve remained within some threshold of the
maximum.

[1] http://169.237.35.250/~dylan/solar/cell1.png

[2] http://169.237.35.250/~dylan/solar/four_points_map5.png

> and if anyone is interested this is part of a dataset that was created and is 
> being visualized with the open source GIS package called GRASS. (yeah for 
> OSS!!)

I've heard of it... but I tend to concentrate on one location at a time.

> thanks in advance, and sorry about the slightly off topic (and probably bone 
> headed) question...

One way I wouldn't characterize this question as is bone-headed ...
finding good modelling equations is tough... whether you use Linux or not.
;)

PS: "Raditation"?

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